Optical microresonator with microcylinder and circumferential coating forming resonant waveguides

ABSTRACT

An optical microresonator and method of forming same includes a microcylinder and a circumferential coating formed on the microcylinder. This coating has a higher index of refraction than the microcylinder and is of such thickness relative to the diameter of the microcylinder that a resonant waveguide is formed such that light optically couples from an optical source waveguide onto the microcylinder.

FIELD OF THE INVENTION

The present invention relates to the field of optical resonators, andmore particularly, to optical microresonators that exhibit whisperinggallery modes.

BACKGROUND OF THE INVENTION

Telecommunications systems incorporate extensive optical fiber networksusing frequency multiplexing/demultiplexing techniques for opticalcommunications signals. These types of optical communications systemsrequire add/drop filters for selecting a single wavelength from complexoptical signals that are typically frequency multiplexed together. Also,optical sensors are used at narrow band frequencies and wavelengths andmay require add/drop or other functionality. These sensors are requiredfor accelerometers, chemical and biological sensors, and similarapplications.

Prior art devices for these add/drop filters and optical sensors includeFabry-Perot structures, waveguide ring resonators, and sphericalresonators. Fabry-Perot structures have been widely used for manyapplications, but have difficult extensions to the multipole. Waveguidering resonators are planar structures that can be fabricated with littlecomplexity and incorporate a simple extension to the multipole. Onedrawback is their high losses. Spherical resonators are small in sizeand have low loss, making them efficient for limited applications. Theyare not efficient, however, for some applications requiring an extensionto multipole filters. Other microcavity geometries incorporatewhispering gallery modes and photonic crystals.

FIG. 1 shows a prior art microsphere 20 positioned adjacent an opticalfiber 22. A 980 nm SMF and 980 nm optical pump are used as an input andthe output is a 1550 nm SMF and 1550 nm laser. The optical fiber 22 istapered and can be brought in contact with the microsphere 20 and theevanescence light from the optical fiber 22 enters the microsphere 20.Air guided region 24 and vestigial cores 26 are shown. The TEill mode ofpropagation occurs along the “equator” or center portion of themicrosphere. This is a well known practice operative in a whisperinggallery mode.

Other examples of prior art microspheres operative in a whisperinggallery modes have been designed. For example, U.S. Pat. Nos. 6,389,197;6,487,233; and 6,490,039 assigned to California Institute of Technology,disclose the use of microspheres based on whispering gallery modemicroresonators or cavities. An optical probe can be evanescentlycoupled into at least one whispering gallery mode of the resonator.Optical energy can also be coupled in a waveguide mode, into theresonator that operates in the whispering gallery mode. For example, afiber in its waveguide mode would couple information to the resonator,e.g., the microsphere. The fiber can be cleaved at an angle to causetotal internal reflection within the fiber. The energy in the fiberforms an evanescent field and the microsphere is placed in the area ofthe evanescent field. If the microsphere resonance is resonant withenergy in the fiber, information in the fiber is effectively transferredto the microsphere. Surface gratings can also be placed on themicrosphere. This is advantageous because microsphere resonators canhave high quality (“Q”) factors and small dimensions. They can be abuilding block for larger fiber optic systems. It is also possible tohave a fiber-coupled laser based on a whispering gallery mode resonatorformed of a laser gain medium and an angle-polished fiber coupler asdisclosed in the '233 patent. The optical fiber can be configured toguide light at both the pump wavelength and a laser wavelength,including an angle-polished facet that forms an angle with respect tothe fiber such that the angle-polished facet is positioned with respectto the other resonator to couple evanescently pump light at the pumpwavelength in the optical fiber into a whispering gallery mode at thepump wavelength, and also evanescently couple light in a whisperinggallery mode at the laser wavelength into the optical fiber.

One prior art improvement over the use of microspheres are toroidmicrocavities. These microcavities can have ultra-high “Q” factors ofabout 100 million and a surface-tension induced microscale cavity.Examples include droplets, silica microspheres, and microtoroids.

Toroid microcavities have been formed by photolithography and etchingtechniques on an oxidized silicon wafer to create silica disks. A gasX_(e)F₂ etch undercuts the silica disks with an induced reflow of thesilica using CO₂ to cause a smooth toroidal periphery. Toroidmicrocavities support whispering gallery type modes on a siliconplatform and can reduce the mode spectrum compared to sphericalmicrocavities. Microtoroids can also exhibit reduced mode volumecompared to microspheres. Two mode-volume compression regimes caninclude slow compression and fast modal compression.

In a tapered fiber coupling, the fiber tapers in a transition fromconventional core guiding regions to air-guiding regions with avestigial core on either end as shown in FIG. 1. It can include couplingboth to-and-from a microtoroid on a chip.

These ultra-high “Q” factor and small mode volume results in highcirculating intensities because of the cavity build-up factor. Opticalfibers that are tapered result in an ultra-low loss and optimum couplingof the microcavities. The cavity build-up factor and non-linearthreshold level can be exceeded as indicated from the equation below:$\left( \frac{P_{cav}}{P_{i\quad n}} \right) = {\frac{\lambda}{\pi^{2}{nR}} \cdot \frac{Q_{ex}}{\left( {1 + \frac{Q_{ex}}{Q_{o}}} \right)^{2}}}$P_(i  n) = 1  mW V_(m) ∼ 650  μ  m³ P_(circ) ∼ 110  WI_(circ) ∼ 2.5  GW/cm²

There have also been some experiments on stimulated Raman scattering inmicrospheres. The stimulated Raman scattering causes red shift of a pump(100 nm shift in a telecommunications band). Threshold levels can betypically 100 microwatts for UHQ microtoroids and high quantumefficiencies result because of an ideal coupling junction. Similarresults can occur with toroid microcavities. The stimulated Ramanscattering for toroid emission is typically single mode.

A prediction of threshold using bulk Raman gain constant (doublyresonant process) can be:$P_{thresh} = {{\frac{\pi^{2}n^{2}V_{eff}}{\lambda_{P}\lambda_{R}{{fgC}(\Gamma)}} \cdot Q_{ex}^{P} \cdot \left( \frac{1}{Q_{t}^{P}} \right)^{2} \cdot \frac{1}{Q_{t}^{R}}}\alpha\frac{V_{eff}}{Q^{2}}}$

A minimum threshold undercoupled could be:Q _(ex) ^(min)=2Q ₀(

T≈11%)

The Raman threshold can also affect the mode volume as follows:$V_{eff} = {{P_{thresh}^{\min} \cdot Q_{o}^{2}}\frac{\lambda_{P}\lambda_{R}{{fgC}(\Gamma)}}{\pi^{2}n^{2}}\frac{4}{27}}$

-   -   P: Raman threshold    -   λ_(p), λ_(R): pump and Raman emission wavelength    -   g: Raman gain coefficient    -   C(Γ): intermode coupling parameter    -   Q: Quality factor of pump and Raman mode

Stimulated Raman threshold can be used to infer the mode volume V_(eff).$V_{eff} = {{P_{thresh}^{\min} \cdot Q_{o}^{2}}\frac{\lambda_{P}\lambda_{R}{{fgC}(\Gamma)}}{\pi^{2}n^{2}}\frac{4}{27}}$

Although spherical resonators, waveguide ring resonators, Fabry-Perotstructures and toroid microcavities have been advantageously used asindicated above, these devices still have limitations when opticalfibers are coupled, even though these devices often are easilyfabricated.

Published patent application no. US 2002/0041730, published Apr. 11,2002, discloses a method for fabricating an optical resonator on anoptical fiber by generating a differential of a physical property, forexample, the diameter, density, refractive index, or chemicalcomposition of a transverse segment of the resonator fiber. This couldinclude some type of grooves forming the resonators. The resonator fibersegment can substantially confine a circumferential optical modepropagating around the resonator fiber segment circumference at leastpartially within the resonator fiber segment. This enables substantialconfinement of a substantially resonant circumferential optical modenear a surface of the fiber. As a result, evanescent optical couplingcan occur between circumferential optical modes and an optical modesupported by the second optical element. Different techniques forspatially, selectively generating the differential could includemasking/etching, masking/deposition, laser machining, laser patterningand combinations of the different processes. It is also possible toinclude a plurality of resonators in the same fiber sufficiently closetogether to enable optical coupling between them to provide a frequencyfilter function for optically coupling multiple optical elements,including optical fibers. Although the optical resonator can providesome coupling, it is limited in its use and may not provide adequatecoupling for input/output functions. Its manufacturing requiresnon-rotating upper and lower capillary tubes to hold a spinning opticalfiber, which may not ensure accuracy and have excess tolerance. Somelimited teaching for using a single, tapered optical fiber near themicrocylinder is also proposed. It also does not address polarizationissues, slower waveguide structures, multiple node contacts, and the useof coatings for imparting waveguide resonance or similar issues.

SUMMARY OF THE INVENTION

In view of the foregoing background, it is therefore an object of thepresent invention to provide an optical microresonator that can beformed as a microcylinder and provide a resonant waveguide operativewith a circumferential coating.

This and other objects, features, and advantages in accordance with thepresent invention are provided by a optical microresonator that isformed as a microcylinder and a circumferential coating formed on themicrocylinder, which has a higher index of refraction than themicrocylinder. This circumferential coating is of such thicknessrelative to the diameter of the microcylinder that a resonant waveguideis formed such that light optically couples from an optical sourcewaveguide onto the microcylinder. The microcylinder is about 8 to about150 microns in diameter. The circumferential coating is about 0.2 toabout 1.0 micron in thickness. The circumferential coating has a filmindex ranging from about 1.4 to about 1.6. The circumferential coatingcan be formed from polymer material such as a plastic material. Also,coupling elements can be formed on the coating to change the directionof light coupled onto the microcylinder.

In another aspect of the invention, an optical source waveguide cancarry light therethrough and couple onto the microcylinder andcircumferential coating. The optical source waveguide forms input andoutput ports, and includes a plurality of microcylinders positionedadjacent the optical source waveguide. Each microcylinder has acircumferential coating with a higher index of refraction than themicrocylinder and of such thickness that light optically couples fromthe optical source waveguide onto the microcylinder to form an add/dropfilter. A method of forming the optical microresonator is also setforth.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention willbecome apparent from the detailed description of the invention whichfollows, when considered in light of the accompanying drawings in which:

FIG. 1 is a fragmentary drawing of a prior art microsphere positionedadjacent an optical fiber to provide coupling between the optical fiberand microsphere.

FIG. 2 is a graph showing a tap field strength weight distribution withdelay of an impulse response for a Gaussian filter and showing thefilter response relative to the frequency offset.

FIG. 3 is a graph showing the impulse response of a 10 GHz bandpassGaussian filter and showing the field coupling weight relative to thedelay in millimeters of glass.

FIG. 4 is a graph showing the band shape for Gaussian and Butterworthfilters.

FIG. 5 is a fragmentary elevation view of a single mode, four-portoptical microresonator coupling system in accordance with one example ofthe present invention.

FIG. 6 is a fragmentary side elevation view showing an opticalmicroresonator having a resonant waveguide formed on a microcylinder,and formed from coupled resonators as circumferential ridges inaccordance with one non-limiting example of the present invention.

FIG. 7 is a high level flowchart illustrating a method of forming theresonant waveguide as coupled resonators on the microcylinder, forexample, as shown in FIG. 6, in accordance with one example of thepresent invention.

FIG. 8 is a fragmentary, partial isometric view of an apparatus used forforming the resonant waveguide on a microcylinder, in accordance withone example of the present invention.

FIG. 9 is a graph showing a modeled whispering gallery mode on amicrocylinder and showing the field strength relative to the distancefrom the surface in microns in accordance with one example of thepresent invention.

FIG. 10 is a graph showing a modeled ridge-guided wave on amicrocylinder of the present invention and showing an axial distance inmicrons relative to a radial distance in microns.

FIG. 11 is a fragmentary side elevation view of a an opticalmicroresonator coupling system used as a filter and showing amicrocylinder having a resonant waveguide formed on a microcylinder inaccordance with one example of the present invention.

FIG. 12 is a graph showing steady state field patterns in accordancewith one example of the present invention and showing the field strengthrelative to the distance from the waveguide axis in microns.

FIG. 13 is a graph showing transient field patterns in a sourcewaveguide and the distance from the waveguide axis and time inpicoseconds in accordance with one example of the optical microresonatorof the present invention.

FIG. 14 is a graph showing transient field patterns in an opticalmicroresonator have a resonator waveguide in accordance with one exampleof the present invention and showing distance from the waveguide axis inmicrons relative to the time in picoseconds.

FIG. 15 is a fragmentary side elevation view of an opticalmicroresonator coupling system and showing optical source and exitwaveguides located close to the optical microresonator.

FIG. 16 is a fragmentary side elevation view of a plurality of opticalmicroresonators coupled together and forming a coupled waveguide,microresonator structure in accordance with one example the presentinvention.

FIG. 17 is a fragmentary isometric view showing an opticalmicroresonator that includes a resonant waveguide and coupling elementof the present invention.

FIG. 18 is another fragmentary, isometric view showing an opticalmicroresonator that has a wide contact, unguided resonator waveguide andcoupling element of the present invention.

FIG. 19 is a fragmentary side elevation view of two microcylinders eachhaving a spiral resonant waveguide and forming a slow-wave opticalmicroresonator of the present invention.

FIG. 20 is a graph showing an EMP model frequency response for a 10micron silica microcylinder showing the resonant waveguide transferfunction on the vertical axis and the wavelength in nanometers on thehorizontal axis in accordance with one example of the present invention.

FIG. 21 is a graph similar to FIG. 20, but showing an EMP modelfrequency response of a 30 micron silica microcylinder and showing ingreater detail the axial and radial pole modes remaining separated forall diameters in accordance with the present invention.

FIG. 22 is a fragmentary elevation view of a coated microcylinder ofabout 9.5 micron with a 0.4 micron polymer coating to form an opticalmicroresonator in accordance with one example of the present invention.

FIG. 23 is a graph showing an EMP model frequency response for a 9.5micron silica microcylinder coated with a 0.4 micron polymer having a1.55 index to form an optical microresonator in accordance with oneexample the present invention.

FIG. 24 is a graph showing a Finite Difference Time Domain (FDTD) modeland showing the insertion loss of an optical microresonator similar tothat shown in FIG. 22 and used as a drop filter in accordance with oneexample of the present invention.

FIG. 25A is a diagram showing two coated, uncoupled opticalmicroresonators used as a drop filter in accordance with one example ofthe present invention.

FIG. 25B is a graph showing a finite difference time domain model withthe insertion loss for the two uncoupled optical microresonators used asa drop filter in accordance with one example of the present invention.

FIG. 26 is a graph showing the response of an optical microresonatorformed from a microcylinder having a 300 nanometer thickness film withan index of 1.55 and showing the optical source waveguide throughput andoptical exit waveguide output, and a filter transfer function (FTF) indecibels as a function of wavelength in nanometers.

FIG. 27 is a graph similar to the graph of FIG. 26, but showing theoptical source waveguide throughput and optical exit waveguide outputfor the 400 nanometer thickness sample.

FIG. 28 is a graph similar to FIGS. 26 and 27 for optical source andexit waveguides, but showing a 500 nanometer thickness.

FIGS. 29-31 are graphs similar to FIGS. 26-28, but with microcylindershaving with a film index of 1.50 instead of the film index of 1.55, asin graphs shown in FIGS. 26-28.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will now be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown. This invention may, however, be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein. Rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. Likenumbers refer to like elements throughout, and prime notation is used toindicate similar elements in alternative embodiments.

The present invention is advantageous over prior art sphericalresonators, waveguide ring resonators and Fabry-Perot structures,including toroid microcavities, and simple cylindrical resonators asdescribed in the incorporated by reference '730 published patentapplication. The present invention is directed to an opticalmicroresonator that includes a resonant waveguide formed on amicrocylinder, for example, spaced resonant elements, such ascircumferential ridges, forming a resonant waveguide on themicrocylinder for coupling to and from optical input and exitwaveguides. These resonant elements could include ridges, some types ofgrooves, etched surface configurations, dielectric lines or otherdielectric placements, or coatings. Whispering gallery modes on amicrocylinder can use a one-dimensional beam propagation coating and aneffective index profile to account for a cylindrical geometry, forexample, with a 120 micron microcylinder, n=1.498, Gaussian mode with8.3 micron mode field diameter, on right microcylinder and immersed inwater, n=1.33. For purposes of explanation, basic functions of aresonant waveguide on a microcylinder in accordance with onenon-limiting example of the present invention are explained.

A waveguide on a microcylinder can form a homogenous waveguide structureand can be extended to complex, coupled structures. Although prior artmicrosphere technology is a simple, natural geometry and readilyavailable because of its wide application in biochemistry and as afiller with concomitant ease of fabrication, microspheres are difficultstructures for use in compound/multipole structures. Microcylinderresonant waveguides of the invention can be formed by ultraviolet laserwriting on a rotating microcylinder, for example, by cutting ridges orexposing to light a photoresist-coated microcylinder, as will beexplained in greater detail below.

In the present invention, light impinges on the microcylinder having theresonant waveguide and can be considered to be guided around the curvedsurface forming the microcylinder without lateral guidance. In oneexample of the present invention, however, lateral spreading isprevented by using the resonant waveguide on the microcylinder andconfining the energy and preventing the energy from moving axially downthe microcylinder and then spreading. In some aspects of the presentinvention, depending on the configuration, it is possible to placespaced, circumferential ridges on the microcylinder, forming resonantelements, e.g., resonators, and thus forming a resonant waveguide. It isalso possible to place a layer of glass on top of the microcylinder toform a resonant waveguide. Circumferential spaced ridges as resonatorscan also be placed on the glass. In other aspects of the presentinvention, it is possible that light can move around the microcylinderagainst its surface and ridges or an extra layer is not required.

In some cases, it is desirable to etch the circumferential ridge for theresonant waveguide around the microcylinder. In one non-limitingexample, a collar of photoresist could be placed on the fiber, which ischemically etched at a fraction of a micron, enough to form a resonantwaveguide. The photoresist could be exposed to light from a laser, forexample. When the photoresist is stripped off, that fiber area that hasnot been etched is untouched glass and forms a resonant waveguide. It isalso possible to couple two microcylinders together using preciselithographic techniques. It is also possible to control the height ofany ridges and control the coupling between resonators forming theresonant waveguide of the optical microresonator. Two coupled resonatorsor ridges could be formed on the same microcylinder, for example, anoptical fiber, by writing two lines or ridges and etching the devices,as compared to difficulties in the prior art that occur when two spheresare positioned adjacent each other. A spiral resonant waveguide could beformed, in accordance with the present invention, to act as a slow wavestructure, such that the speed of light propagating along themicrocylinder is slowed. This is similar to a traveling wave tube.Instead of electromagnetic waves, however, the optical microresonator ofthe present invention is used with light. A helical structure could beformed on the microcylinder as a spiral or other configuration to form aslow wave optical microresonator.

The spiral turn spacing can be configured such that when the next spiralturn occurs, the resultant fields do not couple to the first spiralturn. It is also possible to make a slower optical microresonator usingspiral turns with a wider wrap. Also, two spiral turns could couple toeach other making a slow wave optical microresonator.

The optical microresonator of the present invention is advantageous andalso allows coupling of source and exit optical waveguides along theaxis of the microcylinder. There are different ways to couple thesewaveguides to the optical microresonator, in accordance with the presentinvention. These techniques include configuring a source or exit opticalwaveguide, for example, an optical fiber, perpendicular or transverse tothe axis of the microcylinder. When correctly positioned, any lightreceived within the optical source waveguide couples to themicrocylinder and travels around the microcylinder. It is also possibleto add coupling elements, for example diffraction gratings, as onenon-limiting example, at different angles to the resonant waveguide, forexample, 90 degrees, such that the light propagates and turns orswitches direction. It is also possible to place a perturbation as acoupling element, for example, a 45 degree cut, ridge, diffractiongrating or other perturbation, between two ridges such that lightinitially travels one direction and then travels another direction. Thelight could travel in one direction, and the 45 degree cut orperturbation could cause the light to travel the other direction. Therecould be a sequence of these perturbations or cuts that can be formed byetching. They could be formed on the surface of different resonantelements forming the resonant waveguide. They can also be fabricated asa notch.

It should be understood that if the optical microresonator is wideenough, a light wave will not spread because of its width, and the 45degree (or other degree) perturbations, or other coupling element canstart the light moving around the microcylinder. It is possible to havea wide resonator. The 45 degree lines could be etched or laser formedbumps or grooves on the microcylinder.

The cylindrical optical microresonators of the present invention can beformed by writing a pattern on an optical fiber as it rotates. Thisoptical fiber can be dip coated in photoresist and pulled out while anultraviolet laser exposes the photoresist. During laser writing, theoptical fiber can be rotated and moved axially in a predetermined mannerand any pattern written on it by a fixed position laser, similar to alathe. Etching could occur to remove the resist in selected areas. Ofcourse, the laser could also be movable, but this would require acomplicated control mechanism.

Because it is necessary to have write accuracy to a micron in this typeof process, a fiber ferrule can be used for exact placement. The ferruleis similar to an optical fiber connector and includes a very precisefiber guide in its center. The fiber ferrule can be formed as aprecision ceramic through which the fiber passes. In the presentinvention, first and second spaced ferrules can receive optical fiberand allow it to be fed. Clamps engage and hold the optical fiber withina first ferrule. A chuck can be used for rotating the ferrule and fiber.The process would still be advantageous even if there is some inaccuracyin the chuck positioning because the optical fiber is constrained by theprecisely designed ferrules. Thus, the axis of rotation and the axis ofsymmetry are very close using these ferrules. Although two ferrules areillustrated to control axial movement, more could be used. Also,depending on design, only one need be used.

The fiber can be drawn down to a diameter of about 8 to about 10 micronsfor use as a microcylinder, and that thin a fiber would still be usefulas a microcylinder. Although a range of fiber thickness can be providedfor a microcylinder, an upper limit even as high as about 150 microns ispossible, and a smaller diameter of 8 microns is possible with thepresent invention. The fiber could also be drawn through a photoresistsuch that the surface tension causes the photoresist to spread evenlyalong the fiber. The pressure generated by the surface tension increasesas the fiber radius decreases. In this application, the pressure isabout equal to the surface tension of the fluid divided by the radius ofcurvature. Thus, a smaller fiber would generate a larger amount ofpressure. A laser could expose the photoresist for etching or otherprocessing.

It is well known that light has two possible polarization states thatmay not resonate at the same frequency on a cylindrical opticalmicroresonator of the present invention. It is more desirable, ofcourse, to have light polarized in a single state at a single frequency,such that the resonances operative with the cylindrical opticalmicroresonator have the same frequency for both polarizations.

In the present invention, it is possible to bring the two polarizationstates into degenerancy at the same resonant frequency. This can beaccomplished in one non-limiting example by placing another layer orcoating over the microcylinder. This coating would have the properthickness and proper refractive index, according to end userequirements. The polarization can be tuned and have the samepolarization in both states. For example, with a 10 micron diameterfiber, the polarization resonances are distinct and separate from eachother.

In one computer-modeled example, a layer of coating material with arefractive index of about 1.5 can be placed at about half a micron onthe resonator, although about 0.2 to about 1.0 micron thick coating canbe an acceptable range and be operable depending on end use andmicrocylinder design. The polarization states degenerate. This wouldbring the two polarizations into the same frequency. In this example, itis possible that some polymer material could be formed on the fiber as acoating surface to have a higher index and can be formed as a permanentpart of the structure. For example, polystyrene or other plasticmaterials could be used and positioned over the microcylinder and have athickness for proper polarization.

For purposes of understanding of the present invention, furthertechnical background and a brief explanation concerning fiber wavelengthdivision multiplexed channels is discussed relative to coupled arrays ofresonant waveguide forming by resonators or ridges on the microcylinder.

The fiber communications industry has settled on a telecommunicationsgrid of absolute frequencies where fiber wavelength division multiplexedchannels are located. The communications grid is located on linesseparated by integral multiples of 100 GHz (0.8 mm) from an absolutefrequency of 193.1 THz (1552.52 nm). It is possible to use subdivisionsof this grid, such as lines at 50 GHz spacing, or clusters of closelyspaced wavelengths clustered around a 100 GHz line. As a result, filtersand other components are required for building the networks andcommunication systems based on this WDM channel structure.

For example, a 10 GHz wide (−3 dB double sided, 10 gigabit bit rate)channel, near 1552 nm, is a basic WDM unit that can be added or droppedwithout significant degradation to the channel performance. It is oftennecessary to achieve at least 30 dB isolation from adjacent channelsthat are spaced 50 GHz away. As a non-limiting example of the presentinvention, the optical microresonator coupling system of the presentinvention is described and assumed in one non-limiting example such asshown in FIG. 6 to be a single mode “in”, and a single mode “out”coupling system. It may not be possible to achieve the goal of channeldropping by selectively absorbing or scattering a single channel and notcollecting the lost energy. This assumption is important in thisnon-limiting example because it implies reciprocity between the “in” and“out” single modes.

Typically, the physical size of an optical microresonator is aconstraint, but no physical size limit is assumed in this non-limitingexample. At the present level, the fundamental limits on size can bedetermined by the device physics and sometimes by applicationrequirements.

Linear system theory, closely related mode coupling theory, andelectromagnetic theory are applicable in any design configuration usedfor the present invention. The filter impulse response and frequencyresponse can be chosen to model a problem because these responsesrepresent a general, highly developed theory and provide direct physicalinsight into various configurations that might be used to implement theoptical microresonators of the present invention. In particular, theimpulse response is readily visualized as a sequence of taps along afiber delay line. To simplify this example and enable quick evaluationsof these approaches, it is convenient to use a low couplingapproximation, for example, as a negligible depletion of an input beam.Devices that perform the proper filtering function in the low couplingapproximation can be redesigned to achieve the proper weighting withhigh coupling conditions.

Typically, signals are expressed in a complex, translated-to-basebandrepresentation, and the carrier frequency is not shown. “Impulses” canbe defined as short bursts of a few cycles of carrier signal at, forexample, 1500 nm wavelength. Thus, tap delay can provide a correctbaseband phase and provide a correct carrier phase with orders ofmagnitude more stringent and difficult than the baseband requirement. Adifficulty in fabricating actual optical microresonators, for example,as filters, is maintaining the carrier phase through the structure of afilter that is physically large. The tap structure may be recursive, asin a circulating loop, or it may be an extended structure with a tapweight distribution representing a desired impulse response.

Responses can be limited in the time domain because of size andconstruction complexity, and in the frequency domain because ofcrosstalk and channel isolation. Gaussian models could be used forweighting time and frequency when a nominal weighting model is required.A Gaussian weighting is known to yield compact signals in both domainssimultaneously and represents performance close enough to mostreasonable weighting profiles for an analysis.

One example of a desired bandpass function for a Gaussian 10 GHz channelfilter that is applicable to the present invention is illustrated inFIG. 2. This filter isolates channels at 50 GHz or more spacing. The tapfield strength weight distribution with delay as an impulse response forthis Gaussian filter is shown in FIG. 3.

Filters such as Butterworth, Chebychev, and similar filters havedifferent trade-offs of skirt depth, in-band ripple and/or otherperformance measures. The frequency response of 10 GHz bandwidth filtersof three sample types is shown in FIG. 4. The single pole Butterworth isthe band shape of a filter based on a single coupled resonator. Thisresponse is marginal for DWDM channels (10 Mb/sec channels on 50 GHzcenters). A filter formed of two coupled resonators could produce asecond order Butterworth response when the resonator parameters arechosen appropriately.

Referring again to FIG. 3, this graph shows a better evaluation ofpotential filters operative with the present invention. To approach afilter performance as shown in FIG. 2, a filter could have delay valuescomparable to those illustrated in FIG. 3. In this example, there couldbe a path delay difference equivalent to approximately 30 millimeters ofglass between a first coupling point and a last coupling point.

As an example, a filter could be chosen similar in function as a planarwaveguide having a grating coupler overlay. The frequency of the gratingin this example weakly couples the guided wave to a free space wavepropagating at thirty degrees to the plane of the waveguide. Therelative delay over the length of the grating could be expressed asL_(d)=Lg−Lg*cos (30)/n. Approximately 90 mm of waveguide may be requiredto implement this filter. This example represents a configuration thatmay not be as advantageous for an add-drop filter because it couples tothe wavelength bands simultaneously. Different wavelength bands coupleat different angles less than the 30 degrees in which a chosenwavelength couples. A filter of this free space coupling configurationis more applicable as a wavelength multiplexer/demultiplexer as comparedto an add-drop filter.

In order to function as an add-drop filter, a filter should interactonly with the wavelength of the channel that is switched, and leave allother channels unperturbed. This makes it impractical to construct anadd-drop filter based on coupling from many modes or to many modes. Tobe practical as a single channel, add-drop device, the device shouldcouple single mode to single mode. The example given above could violatethis criterion because the free space output is in effect a continuum ofmodes. The channel being switched couples effectively to one range ofthe modes, but the other wavelengths are perturbed because they coupleto another range of output modes (angles). A similar situation occurswith a multimode waveguide coupler. The operating wavelength couples oneparticular mode to another particular mode, but coupling to other modesets will occur on other wavelength channels.

In the present invention, the resonant structures such as parallelcircumferential ridges, spiral ridges, or a coating, or a combination ofone, two or all three that form a resonant waveguide of the presentinvention, can be used to achieve more compact filter structures whichachieve delays by reusing the same path many times throughrecirculation. Such structures have an impulse response that consists ofan exponentially decaying sequence of pulses spaced by a time equal tothe transit time around the recirculating structure. This sequence ofequally spaced pulses represents a filter with multiple passbandsoccurring periodically in the frequency domain with a frequency spacingor free spectral range equal to the reciprocal of the pulse spacing.Resonant structures forming the resonant waveguide for an opticalmicroresonator can achieve the required long delays in compactstructures.

A single mode, four-port optical microresonator 30 in one non-limitingexample of the present invention is illustrated in FIG. 5. This opticalmicroresonator 30 forms an optical microresonator coupling assemblybecause of the optical source waveguide 32, and optical exit waveguide34. Light is received in the optical source waveguide 32, for example,an optical fiber. The light is received on the microresonator 30 andexits out the waveguide optical exit 34. The resonant structures in somedevices, however, commonly take the form of whispering gallery modes inspheres or planar waveguide rings, but in the present invention, areassociated with the microcylinders. A drawback of microspheres has beentheir use as optical couplers necessary for efficient sphere modelexcitation.

In contrast to microspheres, whispering gallery modes in microcylinderstypically lack the confinement of the fields in the lateral direction.In accordance with one non-limiting example of the present invention,however, confinement can be provided by circumferential ridges forming aresonant waveguide on the surface of the microcylinder. Themicrocylinder could also have a coating. In another aspect of thepresent invention, a resonant waveguide formed from ridges or a spiralof ridges of the same or different material as the microcylinder isadvantageous. Different resonant waveguides could be formed on amicrocylinder and be coupled or uncoupled to each other. For example,spaced groupings of ridges could provide different resonant waveguides.

Following the conventional practice of waveguides formed on planarsurfaces, a waveguide can be formed on a microcylinder by forming aridge of transparent material deposited on the surface of themicrocylinder. If this design is continued for approximately 1.5 micronwavelengths, the ridge can typically be a few microns wide, a micron ortwo thick, and have a refractive index slightly larger than that of themicrocylinder.

An example of a microcylinder structure is shown in the incorporated byreference '730 application, but an improved structure is shown in FIG.6. As a non-limiting example, two resonators as ridges 40,41 are formedon the microcylinder 42 and form a resonant waveguide. Only two ridgesare illustrated for purposes of description, but many could typically beformed. A typical input/output coupling system is formed by using twocoupled waveguides 48,50, formed as optical fibers, in this non-limitingexample. The circles positioned adjacent the ridges indicate crosssections of the optical source waveguide, i.e., input port and opticalexit waveguide, i.e., output port, and operative as couplers. Theresonators or ridges 41, 40 may be directly coupled together by fieldoverlap due to the spatial proximity of the two resonators or ridges.The waveguide can also be formed by a selected, transparent materialwith an index higher than that of the microcylinder body and applied asa coating 40 a, 41 a over the ridges, or in some instances a coating isapplied only over the microcylinder. The coating could be formed frompolyethylene, polyamide, or glass over the ridges 41, 40 or on the fusedsilica microcylinder. Other materials could be used. This coating alonecould operate as the resonant waveguide, or ridges developed into thecoating. Tuning can sometimes be provided by moving the microcylinderand its resonant waveguide relative to the source optical waveguide. Thedashed lines 45 indicate a possible taper (shown exaggerated) that canindicate a taper formed in the microcylinder. It can be microns only butenough to provide tuning. Also, it should be understood that the height,spacing and angle of the ridges could impact tuning and polarizationproperties.

Many resonators or ridges can be fabricated on a single microcylinderwith a high degree of control and flexibility in the coupling betweenthem. For example, complex, multiple filters can be constructed bycascading many resonators to form a number of different resonantwaveguides on a single microcylinder with controlled coupling along themicrocylinder. Tuning could be achieved by tapering the microcylindersuch that adjacent resonators or ridges on separate resonant waveguideshave different frequencies. For example, tuning could also be achievedby mechanically sliding a microcylinder along its axis to change whichseries of ridges or resonators are operable with optical source or exitwaveguides, and thus which optical microresonator is operative with anoptical source waveguide. A slow wave structure could be formed byarranging a long string of resonators or ridges with the proper couplingbetween them. Also, placing a helical, i.e., spiral resonant waveguidestructure on the microcylinder would form an optical slow wave opticalmicroresonator. The coupling between the spiral turns can be controlledby choosing the proper pitch and waveguide width.

Many prior art optical waveguides have been fabricated on planarstructures using conventional planar lithography, photoresist masking,plating and etching techniques. Forming resonant waveguides and similarwaveguide structures on microcylinders, such as shown in FIG. 6,requires different manufacturing processes. In one aspect of the presentinvention, it is possible to fabricate the resonant waveguides usingdirect writing with a focused laser beam.

FIG. 7 is a high level flow chart illustrating basic steps as onenon-limiting example used for fabricating the resonant waveguide on amicrocylinder in accordance with the present invention. The initialmicrocylinder could be provided from silicon, optical fiber material. Itwould include an outer cladding and inner core, and could be about 8 toabout 150 microns or larger in diameter. In one non-limiting step it iscoated with photoresist to a desired thickness (block 60) and placed ina precision rotating apparatus or chuck, similar to a lathe chuck. Thechuck assembly is translated to a small circle of approximately 1 to 10microns at the surface of the microcylinder. The chuck assembly can bemoved longitudinally in a direction of the microcylinder axis as itrotates (block 62). The translation mechanism could be a precisionmotion stage under computer control. A laser beam is modulated to exposethe photoresist, while rotating and moving the microcylinder to producecomplex and useful patterns (block 64). Etching and possibly plating canbe used on the photoresist masks (block 66) to produce a finishedproduct having formed ridges as resonators to form an opticalmicroresonator with a resonant waveguide.

FIG. 8 illustrates one non-limiting example of an apparatus 70 that canbe used for forming an optical microresonator having microcylinderresonators or ridges of the present invention forming a resonantwaveguide. The apparatus 70 can use a laser “lathe” fabricationtechnique with or without photoresist and etching steps. As illustrated,an optical fiber 72 that is to form a microcylinder is fed through firstand second spaced ferrules 74 a, 74 b, which are supported by an upperand lower clamp 76 a, 76 b on a support member 78. The ferrules 74 a, 74b include precision fiber guides through which optical fiber passes,such as drawn by a drive mechanism 79, which includes an appropriatedrive motor. The ferrules are typically formed from ceramic, similar tooptical fiber connector ferrules. The upper clamp 76 a can be designedto allow the ferrule 74 a holding the fiber 76 to rotate with the fiberinside. The lower clamp 76 b can be operative such that the fiberrotates within the ferrule, but the ferrule 74 b does not rotate. Thesupport member 78 is positioned on an x, y, z stage 80. A drivemechanism 81 engages and drives the x, y, z stage 80 and is controlledby a controller 90. The stage 80 allows longitudinal movement along theaxial fiber direction. A chuck and drive mechanism 82 connects to theupper ferrule 74 a. The clamps and ferrule can be designed such that thefiber can be positioned and rotated by the chuck and translatedlongitudinally by the stage. Fiber can be drawn from a fiber supply 83through a photoresist 84, where the fiber is coated. The laser 85provides appropriate light exposure of the coated fiber for furtherprocessing, such as etching, in one non-limiting example, at aprocessing station 86. The fiber can be fixed to the upper ferrule 74 ato allow rotation and longitudinal translation in an accurate andprecise manner driving the laser writing step. Thus, fiber can be drawnfrom supply 83, its movement stopped, then precisely controlled whilelaser writing occurs to make a pattern. It should be understood that thelaser can be operative for machining any ridges or grooves directly onthe fiber.

A non-limiting example of the type of fiber that can be used as amicrocylinder in the present invention is SMF28 or similar single-modefiber coated in photoresist. A non-limiting example of a laser sourcethat can be used in the present invention is a 364 nm laser.

Light can be analyzed that propagates in cylindrical guiding structures,i.e., the resonators or ridges, as described above, or in similarlydesigned microcylinder resonators operative to form a resonantwaveguide. An example could be an infinite microcylinder of radius, r,and refractive index, n₁. The microcylinder can be immersed in a mediumof refractive index, n₂. The coordinate system can be chosen with az-axis parallel to the microcylinder axis and a y origin at the centerof the microcylinder. A whispering gallery type guided wave would beassumed to propagate just inside the microcylinder boundary. This waveis undergoing a continuous reflection from the index discontinuity atthe boundary. A simplifying approximation can be used to replace thecircular microcylinder geometry with an equivalent planar geometry.Because the fields are confined to propagate along the circularboundary, the components at a larger radius would propagateproportionately farther. This is approximately equivalent to a planarsystem with a refractive index that varies linearly with the distancefrom the now planar boundary. This technique can be used to analyzebends in optical waveguides. The effective index for the planarequivalent guide is:

n=n₁y/r, in the region just inside the microcylinder (y<0); and

n=n₂y/r, in the region just inside the microcylinder (y>0).

A one dimensional beam propagation coating model could be constructed torepresent this effective index profile. FIG. 9 shows the modeled resultsobtained for a surrounding index of 1.0 (air) and 1.33 (water) outside a120-micron diameter microcylinder with body index, n₁, of 1.498. This Efield structure exhibits several modes when the surrounding index is1.0. At a 1.33 index, the fields are almost single mode and at a 1.40index there is a clean single mode. The mode for the 1.4 index, however,has some radiation loss as evidenced by the pedestal out to 20 micronson the field pattern outside the microcylinder. A surrounding index of1.35 to 1.4 is desirable for a 120-micron diameter fused silica rod. Thefields are confined to within approximately 3 microns of the surfaceinside the microcylinder and penetrate less than 1 micron outside thesurface. The fields in all cases began as a Gaussian profile with an8.3-micron mode field diameter. In this model, they are propagated 2 mmor about five times around the microcylinder.

An index transformation can be used to analyze the microcylinderpropagation and create resonant waveguides on the cylindrical surface.Because the effective index is directly proportional to the distancefrom the axis, r, a higher effective index region is created byincreasing r. A resonator, i.e., ridge, formed on the microcylinder canbecome a resonant waveguide even though the actual refractive index ofthe material in the ridge is identical or substantially similar to thatof the microcylinder itself. This is in contrast to a ridge on a planarstructure where no low loss guiding is produced unless the index of theridge exceeds the index of the underlying plane.

A parameter that is used to characterize the guiding power of an opticalwaveguide is Δ=(n₁−n₂)/n₁. For the ridge-on-a-microcylinder guide,Δ=(r₁−r₂)/r₁=h/r, where h is the ridge height and r is the microcylinderradius. A typical value for Δ is 0.01. This corresponds to a 0.6 micronhigh ridge on a microcylinder with a 60 micron radius.

Ridge guiding with homogeneous material enables the manufacture of highquality resonant waveguides. For example, only a photoresist mask couldbe applied where a waveguide is desired. The surrounding material couldbe etched to a depth required for the desired index step. A laser couldbe used to expose pertinent sections of the photoresist. No deposition,etching or modification would be required at the waveguide. Thisfabrication technique leaves the critical waveguiding region protectedby the photoresist and unmarred by any processing. Furthermore, theprecision (radius, circularity, etc.) of the original microcylinder ispreserved in this type of process. As previously mentioned, many complexand intricate patterns can be created using this laser “lathe” processfor writing on the photoresist.

The index transformation described above provides the parameters of atransformed step index in the planar waveguide created by amicrocylinder wall. Planar waveguide analysis techniques and theeffective index method could be applied to solve for a wave fielddistribution in the axial (z) direction. A single mode operation for aslab waveguide could follow the function Δ=λ²/8h²n₁ ². In this case, his the width of the planar guide, which is the width of the ridge on themicrocylinder in one example of the present invention. If a reasonablevalue of 5 microns is chosen for a ridge width, the Δ value is D<0.0055for a single mode operation. This corresponds to a 0.33 micron ridgeheight on a 60 micron diameter microcylinder.

This geometry could be a good compromise between lateral confinementunder a ridge and controllable ridge height. This level of detail willdepend, of course, on actual device fabrication techniques and end-usedesign. A computed result for a modeled ridge-guided wave on amicrocylinder is shown in FIG. 10 for a 120 micron diametermicrocylinder, immersed in water, with a 0.33 micron ridge of width 5microns.

In the present invention input-output coupling is possible such as byusing an optical source waveguide, e.g. optical fiber, and optical exitwaveguide, e.g., another optical fiber, for example as shown in FIG. 5.This system is an improvement over prior art coupling techniques usingmicrospheres, or one tapered optical fiber near a microcylinder. Thepresent invention provides an improved optical microresonator couplingsystem having a resonant waveguide on the microcylinder in which energycan be coupled into and out of the microcylinder. Coupling occurs whenthe fields from an optical source waveguide overlap the fields from amicrocylinder resonator forming the resonant waveguide. This requiresproximity between the guiding core of the optical source waveguide andthe guiding core of the microresonator. The interaction length, orpropagation distance in both the source and microresonator waveguideover which this proximity must be maintained, is an important parameterin the coupling relationship. The amount of coupling generally varies asthe square of the interaction length.

Coupler design and implementation can also use a gradual transition froman unperturbed optical source waveguide into the coupling region andback out again through the optical exit waveguide. For example, FIG. 11shows a filter 90 using a microcylinder 91 of about 125 microns with aFree Spectral Range (FSR) of about 4.2 nm. An optical fiber 92 isoperative as the optical source waveguide and has a transition 92 a downto the core, which is placed close to the microcylinder and its resonantwaveguide. The filter throughput at the optical fiber 93 operative asthe optical exit waveguide is shown at the lower portion and occurs atanother transition 93 a down to its core. Light enters the fibertransition 92 a and is coupled onto the microresonator and is outputform the microcylinder through the transition 93 a.

In one example of the present invention, a resonant waveguide could beconsidered to be a single mode waveguide with a field E₂. The sourcecould be considered to be a single mode waveguide with field E₁. Thesymmetric power coupling between the two waveguides is c. The value of ccan be computed from the field patterns and the coupling perturbation bythe equation: $\begin{matrix}{\sqrt{c} = {{- \frac{k\quad{\mathbb{e}}^{{- i}\quad\beta_{2}z}}{N}}{\int{\Delta\quad\left( {{\overset{\rightarrow}{E}}_{1} \cdot {\overset{\rightarrow}{E}}_{2}} \right){\mathbb{e}}^{{- {i{({{\beta\quad 1} - {\beta\quad 2}})}}}z^{\prime}}{\mathbb{d}z^{\prime}}{\mathbb{d}x}{\mathbb{d}y}}}}} & \left. 1 \right)\end{matrix}$Where N is a normalizing constantN=∫({right arrow over (E)} ₁ ·{right arrow over (E)} ₂)dxdy.  2)λ is δn/n for the perturbing index variation.

The effects of mode mismatch on microresonator performance can also beanalyzed, in accordance with the present invention. For example, amicroresonator guide (E2, width 5 microns, D=0.005) can be considered asa perturbation in the field of a ridge waveguide (E₁). A beampropagation analysis can be used with the kernel of equation 1 above asa concentrated source in a single plane parallel to the z-axis. Nomicroresonator losses are introduced in this example. The model mismatchloss between the microresonator mode and the optical source mode can beconsidered the dominant loss. A mode-to-mode overlap of 0.7 causes halfthe coupled power to go back into the optical source guide and half tobe lost in radiation or non-propagation modes. A model calculation forthis arrangement was performed and the steady state field patterns forthe incident mode, transitioned field, and resonator field are shown inFIG. 12.

The graph in FIG. 12 shows steady state field patterns. The graph lineindicative for the transmitted field is plotted as absolute value, suchthat the negative central field is positive. Although the transmittedfield is large, the content of the propagating mode is more than 20 dBbelow the incident field. The correlation coefficient between the inputsource mode and the normalized microresonator field mode is 0.71. Theformation of the field pattern in the source guide is seen in thetransient field pattern shown in FIG. 13. The corresponding fieldbuild-up in the microresonator is shown in the transient field patternof FIG. 14.

These model results are a 50/50 split of the light between scatteredmodes and the propagating mode. It does not represent a 50% loss in themicroresonator, but a 50/50 split between losses and coupling. A 50/50split can be a target for a loss to coupling ratio.

When using the microcylinders as described above, the microcylinders mayexhibit multiple passbands separated by the free spectral range, afrequency interval equal to the reciprocal of the transit time aroundthe microcylinder. Achieving a large free spectral range (FSR) mayrequire a small microcylinder.

As shown in FIG. 15, the zone of contact between the microcylinder 95(of about 10 microns) and the optical source waveguide 96 and opticalexit waveguide 97 are very short for a small microcylinder 95. A 50micron diameter microcylinder, for example, could provide a contactlength of less than 20 microns. Because the power coupling coefficientvaries as the square of the coupling length, this short coupling couldlimit the use of the microresonator in some applications. The multiplepassband, FSR and the passband shape of a filter based on a singlemicroresonator could affect performance. A single microresonator has aLorentzian band shape, which falls off as the first power of thefrequency offset from the band center. This is a slow drop for mostapplications.

Coupling and FSR can raise other issues. FIG. 16 illustrates coupledoptical microresonators as microcylinders, each having a resonantwaveguide. Multiple microresonators are coupled to an optical sourcewaveguide and each other. This is extendable to many microresonators. InFIG. 16, five microcylinders 100 a-e form a coupled waveguidemicroresonator structure 101. In one non-limiting example, the structure101 is a pyramid configuration. Three contacts 102 a, 102 b, 102 c arepositioned at the optical exit waveguide 104. Two contacts 102 d, 102 eare positioned at an optical source waveguide 106. Because themicroresonators are mutually coupled, the coupled fields add coherently.Therefore, the three contacts provide a nine-fold increase in coupledpower. This complex structure, however, does not always maintain theproper phase relationship between all the coupling points (seven in thisexample).

In accordance with the present invention, a coaxial microcylinder tooptical source waveguide coupling can be established. Some of thephasing and contact spacing problems of the structure in FIG. 16 can bealleviated by placing coupled microcylinders concentrically on the samemicrocylinder. But contact with multiple microresonators requires thatthe microcylinder axis lie parallel to the optical source waveguideaxis. Coupling from an optical source waveguide into a microresonatorrequires a coupling element that changes the direction of propagation by90 degrees (or any angle required to direct the light from the sourceguide to the resonator guide when the axes are not parallel).

A coupling element, for example, a diffraction grating or similarstructure, for example, a dielectric line structure as shown in FIG. 17,is one structure possible for achieving this coupling. The couplingelements can couple between waveguide modes and couple from opticalwaveguides to resonators or ridges forming the resonant waveguide.

FIG. 17 shows an optical source waveguide 110 contacting the top of aseries of ridges 112 forming a resonator waveguide on a microcylinder114. The angled series of lines, forming the coupling element, forexample a diffraction grating 116, dielectric line, etched bump, notch,groove or other structure is operative with the resonant waveguide. Insome aspects it is directly formed on the ridge and spaced an integralnumber of wavelengths apart in contact with the optical source guide.The coupling element could be directly on or between the ridges. Theresonators or ridges forming the resonant waveguide may be mutuallycoupled by proximity or by coupling structures overlaid on them. Thecoupling length of this structure is not limited by the microcylindergeometry and coupling lengths are limited only by the precision requiredto maintain precise spacing and phase relationships over the structure.If the waveguide resonators or ridges are spaced sufficiently far apart,there will be no mutual coupling and each acts independently. The powercoupled from the optical source waveguide varies in direct proportion tothe number of resonant waveguides in contact with the optical sourcewaveguide. If there is strong coupling, the coupled power varies as thesquare of the number of resonant waveguides in contact.

It is possible that a ridge forming a resonant waveguide would not haveto be used. If the grating contact zone is long enough, a broadwavefront, e.g., a one dimensional plane wave, propagates around themicrocylinder. Such a wide structure can be designed to have lowdiffraction losses and no waveguiding is needed. The wide contact,unguided resonator structure shown in FIG. 18 is an example.

For this geometry, the coupling is frequency selective because thedirection of the coupled wave steers with wavelength. The frequencyselectivity of this mechanism is determined by the axial length of thecoupling region in wavelengths. The free spectral range is determined bythe circumference of the microresonator in wavelengths. When thecoupling length is large, the circumference of the microcylinder and theresolution of the coupling is sufficient to select a single passbandfrom the micro resonator and reject the undesired spectral bands thatare one or more free spectral ranges away. This structure solves theproblem of achieving sufficient coupling length for good strength ofcoupling and simultaneously solves the problem of multiple passbands inthe microresonators.

Another variation on the basic optical microresonator as described isthe array shown in FIG. 19. The resonant waveguides are a continuousspiral, instead of parallel bands or ridges. The turns of the spiral maybe coupled or uncoupled. This coupling can be controlled by the choiceof width and spacing of the turns or by other coupling structures. Inthis example, the optical source waveguide 200 couples to a resonantspiral waveguide 202, and that guide couples to a second spiral 204,both formed on respective microcylinders 202 a, 204 a. A couplingelement 206, for example a diffraction grating, together with a chosenspiral turn spacing, can be chosen to meet the desired phase matchingconditions between the optical source guide and the spiral slow wavestructure. The coupling element could be a diffraction grating, etchedbump, notches, dielectric lines, or other structure.

The present invention improves upon the prior art opticalmicroresonators such as the published '730 patent application. Thepresent invention can include a resonant waveguide having its ridgesforming grooves such that ridges are aligned in a predetermined mannerto impart a desired polarization, which can also be accomplished throughapplication of a coating in another aspect of the present invention. Thecoating can also be advantageous for waveguide slowing and polarizationeffects. The coupling of ridges with a predetermined groove depth(height), spacing and angle relative to the microcylinder can form aslow wave structure and affect the waveguide coupled resonator and thecoupling mode with another optical source guide. The present inventionof course allows a multiple contact coupled structure as in the exampleof FIG. 16 such that filters can be coupled together.

It is possible that resonant waveguides as ridges (and accompanyinggrooves) do not have to be formed on a microcylinder to form a resonantwaveguide and optical microcylinder and, in the present invention, a“stripe” of optical energy can possibly be placed around themicrocylinder such that the width of the strip of light going around themicrocylinder is not spread and is instead columnated as long as it isnot small relative to the order of the wavelength. It is possible toobtain zero birefringence. FIG. 9, for example, shows a modeledwhispering gallery mode on a microcylinder. Thus, it is possible that aresonant waveguide using ridges may not be necessary on a microcylinderif a wide stripe of light passes around the optical fiber withoutspreading. It would be a function of the width of what is being coupledinto and the distance around the waveguide relative to an angular spreadof optical energy. For example, a large diameter microcylinder with anarrow excitation would not be advantageous because the optical energywould defract as it goes around. It is not dominated by diffractionlosses. The present invention allows a microcylinder resonator and astripe that is wide enough to achieve low enough defraction losses. Thisis a function of the engineering parameters of the design. A coatingwould be even more advantageous.

There are advantageous positioning issues because it is not necessary toposition the optical source waveguide within two microns of a fivemicron wide resonant waveguide formed on the microcylinder. Thus, it isnot critical where the mode or touching is because it will be operable.

It is also possible to have a tapered optical fiber that may or may notinclude a resonant waveguide as a ridge and it can be slid back andforth relative to an optical source waveguide for frequency tuning andselection. It should be understood that some of these systems anddevices as described are polarization dependent and it is desired insome cases to have polarization independence. In accordance with thepresent invention, a coating or layer can be applied to themicrocylinder to produce a birefringence and bring two polarizations intune and alignment such that both polarizations are the same within agiven wavelength range. The coating could be applied over ridges orother resonators forming the resonant waveguide.

It should be understood that when using an optical fiber, a usergenerally does not have control over the polarization. It is possiblethat the ridges or other resonator structure forming a resonantwaveguide on the microcylinder as described before, could be made of theright index material and have the right thickness, and thus contain apolarization independent property. As a result, there are a set ofparameters operable with the resonators, e.g. ridges, that have theright thickness and right refractive index material, and as a result thepolarization independence is established.

In some examples, a ridge by itself with a refractive index the same asthe underlying microcylinder material would form a desired resonantwaveguide. It is possible to form a resonant waveguide out of higherindex material with the proper thickness to set a desired waveguideproperty. For example, a coating could cause some polarized lights topropagate faster and establish a birefringence. In some instances, acoating alone over the microcylinder not only could produce the desiredresonator structure, but also produce the polarization effect and bringpolarization states into degenerancy.

FIGS. 20 and 21 show the EMP model frequency response of a respective 10micron silica microcylinder and a 30 micron silica microcylinder withthe axial and radial pole modes shown and remaining separated for alldiameters.

FIG. 22 shows a non-limiting model for a 9.5 micron cylinder 200 with a0.4 micron polymer coating 202 and the optical source guide 204 adjacentwithin a testing chamber 206.

FIG. 23 shows the EMP model frequency response of the 9.5 micron silicacylinder coated with a 0.4 micron polymer shown in FIG. 22 and having anindex of 1.55 and showing the axial polarization and radial polarizationand showing a good matching of nodes.

FIG. 24 shows a finite difference time domain model with the insertionloss of one optical microresonator as a drop filter and shown next toand adjacent the optical source guide as an optical fiber with theoptical source waveguide (in) and optical exit waveguide (out).

FIG. 25A shows two uncoupled micro resonators 220, 222 as a drop filter224 and the In and Out positions of the optical source guide 226. FIG.25B shows the finite different time domain model using the structureshown in FIG. 25A.

FIGS. 26, 27 and 28 show the response and the filter transform functionas a function of the wavelength for respective 300, 400 and 500nanometer thickness layers with a film index of 1.55 and showing thesource throughport and waveguide output.

FIGS. 29, 30 and 31 show a response for respective 300, 400 and 500nanometer coatings of a 1.50 film index and showing the sourcethroughport and waveguide output.

The coating as used in the present invention could be accomplished bydip coating in a solvent until the solvent dries, leaving the coatingover the microcylinder. This is similar to spraying on a varnish, wherethe solvent evaporates and is left over as the coating after drying.This can be accomplished in a controlled manner in the apparatus of FIG.8. It could also be accomplished before or subsequent to any ultravioletstep in the laser. The circumferential coating could be formed from apolymer, such as a plastic as described before, or a glass. The coatingcould range in one non-limiting example from about 0.2 to about 1.0micron thickness on a microcylinder about 8.0 to about 150 micronsdiameter. The film index could range in one non-limiting example fromabout 1.4 to about 1.6.

This application is related to copending patent applications entitled,“OPTICAL MICRORESONATOR COUPLING SYSTEM AND ASSOCIATED METHOD,” and“APPARATUS AND METHOD FOR FORMING AN OPTICAL MICRORESONATOR,” and“COUPLED WAVEGUIDE OPTICAL MICRORESONATOR,” and “OPTICAL MICRORESONATORWITH COUPLING ELEMENTS FOR CHANGING LIGHT DIRECTION,” and “OPTICALMICRORESONATOR WITH RESONANT WAVEGUIDE IMPARTING POLARIZATION,” and“SPIRAL WAVEGUIDE SLOW WAVE RESONATOR STRUCTURE,” which are filed on thesame date and by the same assignee and inventors, the disclosures whichare hereby incorporated by reference.

Many modifications and other embodiments of the invention will come tothe mind of one skilled in the art having the benefit of the teachingspresented in the foregoing descriptions and the associated drawings.Therefore, it is understood that the invention is not to be limited tothe specific embodiments disclosed, and that modifications andembodiments are intended to be included within the scope of the appendedclaims.

1. An optical microresonator comprising: a microcylinder; and acircumferential coating formed on the microcylinder and having a higherindex of refraction than the microcylinder, and of such thicknessrelative to the diameter of the microcylinder that a resonant waveguideis formed such that light optically couples from an optical sourcewaveguide onto the microcylinder.
 2. An optical microresonator accordingto claim 1 wherein said microcylinder is about 8 to about 150 microns indiameter.
 3. An optical microresonator according to claim 1 wherein saidcircumferential coating is about 0.2 to about 1.0 micron in thickness.4. An optical microresonator according to claim 1 wherein saidcircumferential coating has a film index ranging from about 1.4 to about1.6.
 5. An optical microresonator according to claim 1 wherein saidcircumferential coating is formed from a polymer material.
 6. An opticalmicroresonator according to claim 5 wherein said circumferential coatingis formed from a plastic material.
 7. An optical microresonatoraccording to claim 1 and further comprising coupling elements formed onthe coating to change the direction of light coupled onto themicrocylinder.
 8. An optical microresonator coupling system comprising:an optical source waveguide that carries light therethrough; amicrocylinder positioned adjacent the optical source waveguide; and acircumferential coating formed on the microcylinder and having a higherindex of refraction than the microcylinder and of such thicknessrelative to the diameter of the microcylinder that a resonant waveguideis formed such that light optically couples from the optical sourcewaveguide onto the microcylinder.
 9. An optical microresonator couplingsystem according to claim 8 wherein said optical source waveguide formsinput and output ports, and including a plurality of microcylinderspositioned adjacent the optical source waveguide, each microcylinderhaving a circumferential coating with a higher index of refraction thanthe microcylinder and of such thickness such that light opticallycouples from the optical source waveguide onto the microcylinders toform an add/drop filter.
 10. An optical microresonator coupling systemaccording to claim 8 wherein said optical source waveguide comprises anoptical fiber.
 11. An optical microresonator coupling system accordingto claim 8 wherein said microcylinder is about 8 to about 100 microns indiameter.
 12. An optical microresonator coupling system according toclaim 8 wherein said circumferential coating is about 0.2 to about 1.0micron in thickness.
 13. An optical microresonator coupling systemaccording to claim 8 wherein said circumferential coating has a filmindex ranging from about 1.4 to about 1.6.
 14. An optical microresonatorcoupling system according to claim 8 wherein said circumferentialcoating is formed from a polymer material.
 15. An optical microresonatorcoupling system according to claim 14 wherein said circumferentialcoating is formed from a plastic material.
 16. An optical microresonatoraccording to claim 8, and further comprising coupling elements formed onthe coating to change the direction of light coupled onto themicrocylinder.
 17. A method of forming an optical microresonator, whichcomprises: forming a microcylinder; and adding a circumferential coatingon the microcylinder having a higher index of refraction than themicrocylinder, and of such thickness relative to the diameter of themicrocylinder that a resonant waveguide is formed such that lightoptically couples from an optical source waveguide onto themicrocylinder.
 18. A method according to claim 17, which furthercomprises forming the microcylinder to have a diameter ranging fromabout 8 to about 150 microns in diameter.
 19. A method according toclaim 17, which further comprises forming the circumferential coatingfrom about 0.2 to about 1.0 micron in thickness.
 20. A method accordingto claim 17, which further comprises forming the circumferential coatingfrom about 1.4 to about 1.6 film index over the microcylinder.
 21. Amethod according to claim 17, which further comprises forming thecircumferential coating as a polymer material.
 22. A method according toclaim 17, which further comprises forming the polymer material from aplastic material.
 23. A method according to claim 17, which furthercomprises forming coupling elements on the coating to change thedirection of light coupled onto the microcylinder.